> "Ben Bacarisse" <email@example.com> wrote in message > news:0.7912956cb736cc5e9ead.20121128152922GMT.firstname.lastname@example.org... >> "Existential Angst" <email@example.com> writes: >> >>> "Ben Bacarisse" <firstname.lastname@example.org> wrote in message >>> news:0.ef56b5652decd19bb478.20121128013501GMT.email@example.com... >>>> "Existential Angst" <firstname.lastname@example.org> writes: >> <snip> >>>>> Well, ackshooly I am talking about true random. Bailey and Crandall >>>>> are >>>>> hypothesizing that e, pi et al are true random (I like "intrinsically >>>>> random"), but you and others are apparently arguing that because pi can >>>>> be >>>>> calc'd or generated, it cannot be random. Bailey/Crandall would >>>>> clearly >>>>> disagree with this. >>>> >>>> No, they don't. I am sure they accept the information theoretic >>>> meaning of the word, just as I accept the statistical sense of the term >>>> (especially when in "scare quotes"). >> [I corrected some of my spelling in the above] >>> >>> What is the diffeence between "random" in the information-theoretic >>> context >>> vs. the statistical context? >>> Wouldn't the two be correlatable or translatable in some way? >> >> They are related but they are not the same. I think all >> non-compressible sequences will be statistically random, but not >> vice versa (as pi shows). > > What is compressibility, and what is its significance here?
It refers to the Kolmogorov complexity. In that context, random sequences can't be "compressed" by representing them as machines (usually Turning machines) smaller than the sequence itself. In that sense, numbers like pi are highly compressible: an infinity of digits can be represented in a finite machine.
> So are the digits of pi random or not?
It depends on your definition, but any definition that defines the digits of pi as being truly random is missing something -- there are other sounds definitions in which there are sequence that are very much more random that the digits of pi. By using a relatively weak and purely statistical definition they can be called "random", but most authors (your favourites Bailey and Crandall included) would keep the scare quotes.
> I personally think picking 5 or 10 consecutive digits from the current > trillion digits of pi, and making THAT the basis for a Lotto win would be > more inneresting than a bunch of air-blown pingpong balls....
Try selling that to TV executive!
>> <snip> >>>>> Hasn't pi been calc'd to billions of places already? Seems to me >>>>> that's >>>>> enough random numbers to last people for a while.... lol >>>> >>>> Does the lol mean you are joking? >>> >>> Well actually, the wiki article I linked says pi has been calc'd to a >>> *trillion* digits. >>> The point being, if you need a random sequence, for whatever purpose, you >>> can just sort of pull them "off the shelf", from anywhere in the >>> sequence. >>> A trillion numbers oughtta do ya.... >> >> The problem is the size of the shelf. It's much simpler to link to >> small PRNG algorithm than to provide access to a pre-computed large >> sequence. >> >> <snip> >>>> Good quality, hardware-generated random number sequences (if our current >>>> understanding of quantum effects is correct) are random in a different >>>> way to the digits of pi. It helps if the terminology is be able to >>>> distinguish between them. >>> >>> Which harks back to the above. >>> Couldn't you take a single photon slit experiment, sample the results >>> "byte-wise", ie, record every diffraction result in groups of 5, and let >>> those five zero's/one's represent a base 10 digit? Then, you'd have the >>> photon slit experiment generate irrational-number-like randomness. >> >> Why 5? > > Well, however many binary places it takes to to make the digit 9 -- 4 > places?? lol
Yes, 4, and loop (by rejecting all 4 bits) three times in every eight when the result is > 9. That's the simplest way.
>>> In that sense, information-theoretic randomness (if you would charactize >>> the >>> photon exp as "informational") and statistical randomness could be >>> translatable? >> >> I don't know what you mean by "translatable". > > In the sense that every 4 photon trials could be used to specify a base 10 > digit,ergo a random generator.
Not every 4, at least using the simple method. You have to deal with the case that the four bits specify a digit > 9 and the simplest way is to throw the 4 bits away and try again.